Question: Lennox owns a big apple orchard. She ships her apples to various markets using a fleet of trucks. Every week, each truck goes on $3$ trips, and for each trip Lennox gets $300$ dollars. On a single trip, a truck delivers $50$ packs, and each pack contains $12$ kilograms of apples. Overall, Lennox sells $4500$ dollars worth of apples in a week. How much does Lennox get for a single kilogram of apples?
There can be many ways to solve this problem. Here, we will do this by thinking about units. Let's say apples cost $x\,\dfrac{\text{dollars}}{\text{kilogram}}$. We are given that Lennox makes $300\,\dfrac{\text{dollars}}{\text{trip}}$. How can we relate these two quantities with an equation? $\begin{aligned} x\,\dfrac{\text{dollars}}{\text{kilogram}}\cdot y\,\dfrac{\text{kilograms}}{\text{trip}}=300\,\dfrac{\text{dollars}}{\text{trip}} \end{aligned}$ So in order to find the rate of dollars per apples $x$, we need to figure out $y$, which is the rate of apples per trip. Notice what other information we are given: $3\,\dfrac{\text{trips}}{\text{truck}}$ $50\,\dfrac{\text{packs}}{\text{trip}}$ $12\,\dfrac{\text{kilograms}}{\text{pack}}$ $4500\,\text{dollars}$ Which of these quantities can help us calculate a rate whose units are $\dfrac{\text{kilograms}}{\text{trip}}$ ? We can combine the following quantities: $\begin{aligned} 50\,\dfrac{\cancel\text{packs}}{\text{trip}}\cdot 12\,\dfrac{\text{kilograms}}{\cancel\text{pack}}=600\,\dfrac{\text{kilograms}}{\text{trip}} \end{aligned}$ Now we can plug that in the original equation: $\begin{aligned} x\,\dfrac{\text{dollars}}{\text{kilogram}}\cdot 600\,\dfrac{\text{kilograms}}{\text{trip}}&=300\,\dfrac{\text{dollars}}{\text{trip}} \\\\ x\,\dfrac{\text{dollars}}{\text{kilogram}}&=\dfrac{300}{600}\,\dfrac{\text{dollars}}{\cancel\text{trip}}\dfrac{\cancel\text{trips}}{\text{kilogram}} \\\\ x\,\dfrac{\text{dollars}}{\text{kilogram}}&=0.5\,\dfrac{\text{dollars}}{\text{kilogram}} \end{aligned}$ In conclusion, Lennox gets $0.50$ dollars per kilogram of apples.